Home
Class 10
MATHS
The radius of the base of a right circul...

The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base. The distance of the boundary of the surface from the centre of the base of the frustum is `sqrt(h^(2) + (r^(2))/9)`. Show that the volume of the frustum is 13/27`pir^(2)h`.

Text Solution

Verified by Experts

The correct Answer is:
`13/27pir^2h`
Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (SUBJECTIVE PROBLEMS) (LONG ANSWER TYPE)|4 Videos

  • SURFACE AREAS AND VOLUMES

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (INTEGER/NUMERICAL VALUE TYPE)|10 Videos

  • SURFACE AREAS AND VOLUMES

    MTG IIT JEE FOUNDATION|Exercise EXERCISE (SUBJECTIVE PROBLEMS) (VERY SHORT ANSWER TYPE)|10 Videos

  • STATISTICS

    MTG IIT JEE FOUNDATION|Exercise Olympiad/HOTS Corner|12 Videos

  • TRIANGLES

    MTG IIT JEE FOUNDATION|Exercise Olympiad /HOTS Corner|15 Videos

Similar Questions

Explore conceptually related problems

The radius of the base of a right circular cone is r.It is cut by a plane parallel to the base at aheight h from the base.The slant height of the frustum is sqrt(h^(2)+(4)/(9)r^(2)) .Show that the volume of 13 the frustum is (13)/(27)pi r^(2)h

The radius of the base and the height of a right circular cone are doubled. The volume of the cone will be

A plane parallel to the base of a cone cuts its axis in the ratio 2:1 from its base. The ratio of the volume of the lower part of the cone to that of the upper part is

The height of a right circular cone is 20 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/8 of the volume of the given cone, at what height above the base is the section made?

The radius of base of a cone is r and height is h. Find its volume.

The radius of base of a right circular cone is 2 metres and its height is 6 meters. Find its curved surface and volume.

A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base . The ratio of the volume of the smaller cone to the whole cone is

In a right circular cone, the cross - section made by a plane parallel to the base is a (A) Circle (B) Frustum of a cone (C) Sphere (D) Hemisphere

The base radius and height of a cone is 5cm and 25 cm respectively. If the cone is cut parallel to its base at a height of h from the base. If the volume of this frustum is 110 cm3 . Find the radius of smaller cone?